• Posted by Konstantin 10.01.2012 No Comments

    It is not uncommon when a long-running scientific study or an experiment produces results which are, at best, uninteresting. The measured effect may be too weak to be reported on convincingly given the data at hand. None the less, resources have been put into it, many man-months have been spent, and thus a paper must be published. The researcher must therefore present his results in a way convincing enough for the reviewers to be lulled into acceptance.

    The following are the three best methods for doing that (and I have seen those being used in practice). Next time you read someone's paper (or write your own), keep them in mind.

    1. Use an irrelevant (and preferably strict) hypothesis test.
      Suppose you want to show that a set of measurements in one group differs from the set of measurements in the other group. The typical approach here is the T-test or the Wilcoxon test, both of which detect whether elements in one group are on average greater than those in the other group. If, however, you find that the tests fail on your data (i.e., there is no easily detectable difference in measurement magnitudes), why don't you try something like theĀ Kolmogorov-Smirnov test, which checks whether the distributions of the two groups are different. It is a much stricter condition. In fact the tiniest outlier in your data will easily get you a low p-value and thus something to stick in the face of a reviewer. If even the KS test did not work, try testing something even less relevant, such as, whether your data is normally distributed. Most probably it is not, here's your low p-value! Remember - the smaller your p-values, the better is your paper!
    2. Avoid significance testing completely
      If you can't get a low p-value anywhere, do not worry. Significance testing is going somewhat out of fashion nowadays anyway, so it is possible to avoid it and still sound convincing. If one group of measurements has 40% of successes and the other has 42% - why not simply present those two numbers as obvious proof that the second group is better. Using ratios is also a smart idea. Say, some baseline algorithm has a 1% chance of success. You now test your algorithm and discover that out of 10 trials it had 1 success. That means your algorithm has just demonstrated a 10% success rate, which is ten times better than the baseline! Finally, ROC curves can often be used to hide the fact that your data is too tiny to make any conclusions. No one really ever checks for significance of those.
    3. Sweep multiple testing under the carpet
      If you are analyzing a dataset with 1000 attributes and 50 datapoints, it is not really very surprising if one of those attributes will seem "interesting" (e.g. highly correlated with the target effect) purely by chance - there is often nothing significant in finding one out of a thousand. However, if you only mention that one (or perhaps 10-50) of the original attributes, your results will magically become significant and no reviewer will be able to catch your cheating.

    There are certainly more, and I'll keep the post updated if I come up with a worthy addition. If you have something to add, please do comment.

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